The percent, as indicated in the formula, is always expressed as a decimal value rather than in percent form. The base is sometimes considered the original value. It is the number that you are taking a percentage of. The amount is sometimes thought of as the final answer. Let's lok at a few preliminary examples to make sure you understand how the percent formula works before moving on to the word problems.

What number is 12% of 80?

The percent, written as a decimal is 0.12. The base is 80 and the amount is what we are looking for. So we have

(0.12)(80) = 9.6.

4.515 is 4.3% of what number?

The percent, written as a decimal is 0.043. The base is not known and the amount is 4.515. So we have

The percent is what we are looking for. The base is 400 and the amount is 3.2. So we have

Recall that in the percent formula, percents are written as decimals. So the decimal form is 0.008 which means in percent form we have 0.8%.

These three examples have shown you how to solve for each piece of the percent formula. We now need to apply this information to solving word problems. Remember, the main task is to identify each piece of the percent formula and then solve as we did above. Now let's use this process to work a word problem.

Suppose a retailer buys a coat for $80 and then sells it for $120. What is the percent of markup on the coat?

The problem is telling us that we want to know the percent value, so we need to identify the base and the amount to solve the problem. The value of $80 is our base. We have to be careful here because $120 is not the amount. When we take a percentage of $80, we then add that to the cost of the coat to get the selling price. In other words, the coat has been marked up $40. That is the amount we should be using. So we have the formula

Remember that when we solve the percent formula for a percent, it gives us a decimal value that we have to change into a percent. In this case, the coat has been marked up 50%.

Examples

What is the price of an item that was discounted 20% if the original price was $2500?

What is your answer?

After counting tools and parts in his garage, Tom found that 168 pieces had rusted. There were 300 tools and parts total in the garage. What percentage of his tools were rusted?

What is your answer?

Examples

A bicycle was reduced by 25% or $55 from its original price. What was the original price?

What is your answer?A. $36.25B. $220.00C. $68.75D. $165.00

Kathy is a waitress at a local restaurant. At the end of the day, she adds the receipts from her station and finds that customers spent a total of $630 before tips. She then adds the tips she received for the day and finds that she has $110.25. What percent of total sales were Kathy’s tips?

What is your answer?A. 17.5%B. 0.175C. 5.7%

Solving percent word problems comes down to being able to correctly identify the three pieces of the percent formula. Always read the problems thoroughly. In some cases, the numbers given in the problem cannot be used exactly as they are. Think through the problems carefully to find out what the base and amount values are. Correctly identifying those two pieces will most likely result in correct solutions each time.